When we were presented this problem the very first thing we had to do was write down questions we had about the question given. Things we didn't understand or wanted clarification on. After that we shared and answered them as a group.
My initial attempt was to try and factor the equation, for some reason. When we shared with our group our process a lot of us had empty pages and we weren't really sure what we were doing. After a while of brainstorming and factoring correctly, Mr. Carter helped us out by pointing at a graph and what we could do with it. Plot the points!
We started with the basic y and x intercepts, and made our parabola, then we sketched out a few rectangles inside the parabola. To find the largest area I initially found it the easiest way was just to count the squares inside the box. But it wouldn't give me the area. I knew which one it would be though. So we then plugged it into the equation. After plugging it in, we were a little stuck because we thought that was the final estimated area. We then realized that there could be super tiny points like 1.1, 1.2, 1.3, that could have the largest area instead of the whole number. So we created a x and y table. We stopped calculating them when the number began the become lower, so then we found the closest answer. The function we used to find this was, A=16x-x^3.
Our initial attempts to finding the perimeter was just plugging in the equating for perimeter: P=2(x+y). Then we simplified the function to, P=-2x^2+2x+32. We then found the max vertex which gave us the max perimeter.
We new these functions were correct because it was giving us the correct answers when plotting them on the graph.